## Concentration of solutions

When a solid dissolves in a liquid a mixture is formed. The solid that dissolves in a liquid is called the **solute**, the liquid is called the **solvent** and the mixture formed is called the **solution**. The “strength” of the solution formed is called its concentration. For example, a cup of water that contains 5 spoons of sugar has a higher concentration of sugar than one that contains 2 spoons of sugar. In this case, sugar is the solute and the water is the solvent.

The **concentration of a solution** is the amount of solute dissolved in a solvent.

The amount of solute in the solution can be expressed in terms of moles or as a mass in grams. The volume of solution is usually expressed in dm^{3}, whereby 1 dm^{3} = 1 000 cm^{3}.

### Concentration of a solution using number of moles

The **molar concentration** of a solution is the number of moles of solute in 1 dm^{3} of a solvent.

#### Formula for calculating concentration in terms of moles

$latex Concentration = \frac{Number\ of\ moles\ of\ solute}{volume\ of\ Solvent}$

The units are mol/dm^{3}.

#### Question

27 g of aluminium burns in chlorine to form 133.5 g of aluminium chloride.

- What mass of chlorine is present in 133.5 g of aluminium chloride?
- How many moles of chlorine atoms is in 133.5 g of aluminium chloride?
- How many moles of aluminium atoms are present in 27 g of aluminium?
- Use your answers from above to find the simplest formula of aluminium chloride.
- 2 000 cm
^{3}of an aqueous solution is made using 13.35 g of aluminium chloride. What is its concentration in moles per dm^{3}?

#### Answer

- We are given that 27 g of aluminium burns in chlorine to form 133.5 g of aluminium chloride.Therefore, mass of chlorine = mass of aluminium chloride – mass of aluminium
= 133.5 g – 27 g

= 106.5 g

- We know that:
- the mass of chlorine in 133.5 g of aluminium chloride = 106.5 g.
- molar mass of chlorine atoms = 35.5 g/mol

$latex Number\ of\ moles\ = \frac{mass}{molar\ mass}$

$latex = \frac{106.5\ g}{35.5\ g/mol}$

= 3 moles of chlorine atoms.

- $latex Number\ of\ moles\ = \frac{mass}{molar\ mass}$$latex = \frac{27\ g}{27\ g/mol}$
= 1 moles of aluminium atoms.

- Since the ration of aluminium:chlorine in aluminium chloride = 1:3 the simplest formula of aluminium chloride is AlCl
_{3}. - The concentration is needed in mol/dm
^{3}so we convert the given mass to moles and the given volume to dm^{3}.$latex Volume = \frac{2\ 000\ dm^3}{1\ 000}$= 2 dm

^{3}$latex Number\ of\ moles = \frac{mass}{molar\ mass}$

$latex = \frac{13.35}{27 + (35.5 \times 3)}$

= 0.1 moles of aluminium chloride.

$latex Concentration = \frac{number\ of\ moles}{volume}$

$latex = \frac{0.1}{2}$

= 0.05 mol/dm

^{3}

### Concentration of a solution using grams

The **mass concentration** of a solution is the mass of solute in 1 dm^{3} of a solvent.

#### Formula for calculating concentration in terms of moles

$latex Concentration = \frac{Mass\ of\ solute}{volume\ of\ Solvent}$

The units are g/dm^{3}.

#### Example – A solution contains 23 grams of sodium chloride in 1 dm^{3} of water. Find its concentration in g/dm^{3}.

$latex Concentration = \frac{Mass\ of\ solute}{volume\ of\ Solvent}$

$latex = \frac{23}{1}$

= 23 g/dm^{3}.

### Molarity of a solution

The **molarity of a solution** (M) is its molar concentration.

This means that:

- a 1 M solution has a concentration of 1 mol/dm
^{3}. - a 5 M solution has a concentration of 5 mol/dm
^{3}.

### Calculating amount of solute dissolved in a solution, given its concentration

Given the concentration and volume of a solution we can find the number of moles of solute as follows:

Number of moles = Concentration × Volume

N = CV

#### Example – How many moles of solute are in a 500 cm^{3} of solution, of concentration 2 mol/dm^{3}?

V = 500 cm^{3} = 0.5 dm^{3}

N = CV

= 2 × 0.5

= 1 mole.

#### Example – How many moles of solute are in 2 litres of solution, of concentration 0.5 mol/dm^{3}?

V = 2 litres = 2 dm^{3}

N = CV

= 2 × 0.5

= 1 mole.